Families of K3 surfaces and Lyapunov exponents

2014/12/04 by Simion Filip, Filip, Simion
Mathematics · #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.DS #math.GT

paper · pdf · doi:10.48550/arxiv.1412.1779

35 pages, 1 figure

arxiv created 2015/02/10 · arxiv updated 2015/02/11

Abstract

Consider a family of K3 surfaces over a hyperbolic curve (i.e. Riemann surface). Their second cohomology groups form a local system, and we show that its top Lyapunov exponent is a rational number. One proof uses the Kuga-Satake construction, which reduces the question to Hodge structures of weight 1. A second proof uses integration by parts. The case of maximal Lyapunov exponent corresponds to modular families, given by the Kummer construction on a product of isogenous elliptic curves.

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